Dimensional analysis of a permittivity measurement probe
Dimensional analysis of a permittivity measurement probe
复制标题
介电常数测量探头的尺寸分析
DOI：
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发表时间：
2002
影响因子：
5.6
通讯作者：
R. McClendon
中科院分区：
文献类型：
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作者：
P. G. Bartley;S. Nelson;R. McClendon
开放式同轴线探头提供了一种方便的方法来确定许多材料在相对较宽的频率范围内的介电特性。正因为如此，人们对了解探针与其所插入的材料之间的相互作用给予了很大的关注。本文对一种广义的开放式同轴线探头进行了量纲分析。应用Buckingham /spl Pi/-定理，发现探针/介电界面的导纳随频率的变化是一个单一的无量纲变量的函数。这一事实大大简化了探测器的建模。该问题由频率和介电常数两个变量的拟合模型简化为一个无量纲变量。此外，量纲分析还揭示了同样的结果适用于任何介电常数测量探头，其中探头的导纳是介电常数，频率和任意数量的线性尺寸的函数。
Open-ended coaxial-line probes provide a convenient means of determining the dielectric properties of many materials over a relatively wide frequency range. Because of this, much attention has been given to understanding the interaction of the probe and the material which it is inserted into. In this paper, a dimensional analysis was performed on a generalized open-ended coaxial-line probe. Applying the Buckingham /spl Pi/-theorem revealed that the admittance of the probe/dielectric interface, scaled by the frequency, is a function of a single dimensionless variable. This fact greatly simplifies the modeling of the probe. The problem is reduced from fitting a model of two variables, frequency and permittivity, to one dimensionless variable. In addition, the dimensional analysis also revealed that the same results hold for any permittivity measurement probe where the admittance of the probe is a function of permittivity, frequency, and any number of linear dimensions.